Resolution improvements with bigger sensors

There was a poster on DPR who made the claim that the resolution of a good lens on a full frame camera would be 1.5 times that of the same lens on a APS-C camera with the same pixel count. I thought the improvement would be less than that. We debated a while, and then I realized I had a tool, developed for the depth of field (DOF) work, that would give us the answer with very little programming.

I set up the lens/sensor simulator for a full frame camera with a pixel pitch of 4.5 micrometers (um), no AA filter, 100% fill factor, with a simulated Zeiss Otus 55 mm f/1.4 lens focused at 3 m.

The horizontal axis is subject distance. The Otus’s sharpest f-stop is f/2, and the peak MTF50 is about 1780 cycles per picture height.

The same number of pixels on an APS-C sensor would require a 3 um pitch, and here’s what we’d see on a FF camera:

If we convert that to cycles/picture height for an APS-C sensor, we get:

The peak value rises to 1330 cy/ph. So, going to full frame with the same number of pixels would improve the resolution by (1780/1330) – 1, or 34% — not 50%.

Other f-stops can act as a stand-in for lenses of inferior sharpness.

Consider the f/11 case. The 4.5 um camera peaks at 1250 cy/ph, and the 3 um camera hardly any higher. When we derate the 3 um FF camera to a 3 um APS-C camera, we see almost a 50% improvement. That’s because, with the lens stopped that far down, the sensor pitch’s effect on the MTF50 is much less important than the lens’, and losing lens coverage really hurts.

If we make the lens a 55mm one modeled after the Nikon 85/1.4 G, here’s what we see:

Now the best-sharpness improvement is 1460/1050 – 1 or 39%.

And the Nikon is not a terrible lens by any means.

If we convert the pixel pitches and sensor sizes to pixel count, we can see that

we’ve been talking about 42 megapixel cameras. You can buy an AA-less FF 42 MP camera: the Sonay a7RII. You can’t buy an APS-C 42 MP camera, with or without an AA filter.

Let’s change the numbers to what works out to 24 MP. You can buy a 24 MP APS-C camera without an AA filter: the Sony a6300. You can — or could, at least — buy a FF 24 MP camera with no AA filter from Sony, the RX-1R.

First, with the sharper lens:

The peak sharpness for the FF camera is about 1580 cy/ph, and that of the APS-C camera is 1240. 1580/1240 – 1 is 27%.

With the Nikon lens:

The peak FF MTF50 is 1350. The peak APS-C number is 1000. That’s 35% improvement for full frame.

Comments

I often need substantial depth of field, and shoot at f8 and f11 regularly. Diffraction and shutter speed are constant issues. In real-world shooting, it often seems like APSC and full frame become more equal in resolution in this part of the shooting envelope.

APSC at f8 edges close to full frame resolution at f11 (with roughly equivalent depth of field). From your graphs, the difference becomes more like 17 percent at 42 MP and 15 percent at 24 MP, if I read the numbers correctly.

Of course, comparing 24MP APSC (like on the a6xxx cameras) to the 42MP of the A7RII, the resolution difference, even with the one stop “handicap,” seems to increase back to about 23 percent. On the other hand, the APSC camera has some hand-holdability advantage because of the higher shutter speed.

I my view when it comes to fast lenses it’s more interesting to compare them at equivalent setting wide open rather than at their best settings. So if you compare the same Otus at f/2 on FF and f/1.4 on APS-C the difference is going to be much bigger, close to 2x according to your graphs.